Properties

Label 9576.2.a.bp.1.2
Level $9576$
Weight $2$
Character 9576.1
Self dual yes
Analytic conductor $76.465$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9576,2,Mod(1,9576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9576, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9576.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9576.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(76.4647449756\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 9576.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.23607 q^{5} -1.00000 q^{7} +O(q^{10})\) \(q+3.23607 q^{5} -1.00000 q^{7} -0.763932 q^{11} -5.23607 q^{13} +2.76393 q^{17} +1.00000 q^{19} +1.23607 q^{23} +5.47214 q^{25} -0.472136 q^{29} -8.47214 q^{31} -3.23607 q^{35} -8.94427 q^{37} +2.00000 q^{41} -4.00000 q^{43} +2.47214 q^{47} +1.00000 q^{49} +8.47214 q^{53} -2.47214 q^{55} -8.00000 q^{59} -0.472136 q^{61} -16.9443 q^{65} +5.23607 q^{67} -10.4721 q^{71} -4.47214 q^{73} +0.763932 q^{77} +2.29180 q^{79} +2.00000 q^{83} +8.94427 q^{85} +6.94427 q^{89} +5.23607 q^{91} +3.23607 q^{95} -3.23607 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{5} - 2 q^{7} - 6 q^{11} - 6 q^{13} + 10 q^{17} + 2 q^{19} - 2 q^{23} + 2 q^{25} + 8 q^{29} - 8 q^{31} - 2 q^{35} + 4 q^{41} - 8 q^{43} - 4 q^{47} + 2 q^{49} + 8 q^{53} + 4 q^{55} - 16 q^{59} + 8 q^{61} - 16 q^{65} + 6 q^{67} - 12 q^{71} + 6 q^{77} + 18 q^{79} + 4 q^{83} - 4 q^{89} + 6 q^{91} + 2 q^{95} - 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 3.23607 1.44721 0.723607 0.690212i \(-0.242483\pi\)
0.723607 + 0.690212i \(0.242483\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.763932 −0.230334 −0.115167 0.993346i \(-0.536740\pi\)
−0.115167 + 0.993346i \(0.536740\pi\)
\(12\) 0 0
\(13\) −5.23607 −1.45222 −0.726112 0.687576i \(-0.758675\pi\)
−0.726112 + 0.687576i \(0.758675\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.76393 0.670352 0.335176 0.942156i \(-0.391204\pi\)
0.335176 + 0.942156i \(0.391204\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.23607 0.257738 0.128869 0.991662i \(-0.458865\pi\)
0.128869 + 0.991662i \(0.458865\pi\)
\(24\) 0 0
\(25\) 5.47214 1.09443
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.472136 −0.0876734 −0.0438367 0.999039i \(-0.513958\pi\)
−0.0438367 + 0.999039i \(0.513958\pi\)
\(30\) 0 0
\(31\) −8.47214 −1.52164 −0.760820 0.648963i \(-0.775203\pi\)
−0.760820 + 0.648963i \(0.775203\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.23607 −0.546995
\(36\) 0 0
\(37\) −8.94427 −1.47043 −0.735215 0.677834i \(-0.762919\pi\)
−0.735215 + 0.677834i \(0.762919\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.47214 0.360598 0.180299 0.983612i \(-0.442293\pi\)
0.180299 + 0.983612i \(0.442293\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 8.47214 1.16374 0.581869 0.813283i \(-0.302322\pi\)
0.581869 + 0.813283i \(0.302322\pi\)
\(54\) 0 0
\(55\) −2.47214 −0.333343
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.00000 −1.04151 −0.520756 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) 0 0
\(61\) −0.472136 −0.0604508 −0.0302254 0.999543i \(-0.509623\pi\)
−0.0302254 + 0.999543i \(0.509623\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −16.9443 −2.10168
\(66\) 0 0
\(67\) 5.23607 0.639688 0.319844 0.947470i \(-0.396370\pi\)
0.319844 + 0.947470i \(0.396370\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −10.4721 −1.24281 −0.621407 0.783488i \(-0.713439\pi\)
−0.621407 + 0.783488i \(0.713439\pi\)
\(72\) 0 0
\(73\) −4.47214 −0.523424 −0.261712 0.965146i \(-0.584287\pi\)
−0.261712 + 0.965146i \(0.584287\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.763932 0.0870581
\(78\) 0 0
\(79\) 2.29180 0.257847 0.128924 0.991655i \(-0.458848\pi\)
0.128924 + 0.991655i \(0.458848\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 2.00000 0.219529 0.109764 0.993958i \(-0.464990\pi\)
0.109764 + 0.993958i \(0.464990\pi\)
\(84\) 0 0
\(85\) 8.94427 0.970143
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.94427 0.736091 0.368046 0.929808i \(-0.380027\pi\)
0.368046 + 0.929808i \(0.380027\pi\)
\(90\) 0 0
\(91\) 5.23607 0.548889
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.23607 0.332014
\(96\) 0 0
\(97\) −3.23607 −0.328573 −0.164286 0.986413i \(-0.552532\pi\)
−0.164286 + 0.986413i \(0.552532\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.18034 0.415959 0.207980 0.978133i \(-0.433311\pi\)
0.207980 + 0.978133i \(0.433311\pi\)
\(102\) 0 0
\(103\) −16.4721 −1.62305 −0.811524 0.584319i \(-0.801362\pi\)
−0.811524 + 0.584319i \(0.801362\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −15.4164 −1.49036 −0.745180 0.666863i \(-0.767637\pi\)
−0.745180 + 0.666863i \(0.767637\pi\)
\(108\) 0 0
\(109\) −8.94427 −0.856706 −0.428353 0.903612i \(-0.640906\pi\)
−0.428353 + 0.903612i \(0.640906\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 10.9443 1.02955 0.514775 0.857325i \(-0.327875\pi\)
0.514775 + 0.857325i \(0.327875\pi\)
\(114\) 0 0
\(115\) 4.00000 0.373002
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.76393 −0.253369
\(120\) 0 0
\(121\) −10.4164 −0.946946
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.52786 0.136656
\(126\) 0 0
\(127\) −11.2361 −0.997040 −0.498520 0.866878i \(-0.666123\pi\)
−0.498520 + 0.866878i \(0.666123\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 8.47214 0.740214 0.370107 0.928989i \(-0.379321\pi\)
0.370107 + 0.928989i \(0.379321\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.47214 0.211209 0.105604 0.994408i \(-0.466322\pi\)
0.105604 + 0.994408i \(0.466322\pi\)
\(138\) 0 0
\(139\) 8.94427 0.758643 0.379322 0.925265i \(-0.376157\pi\)
0.379322 + 0.925265i \(0.376157\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.00000 0.334497
\(144\) 0 0
\(145\) −1.52786 −0.126882
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.52786 −0.616707 −0.308353 0.951272i \(-0.599778\pi\)
−0.308353 + 0.951272i \(0.599778\pi\)
\(150\) 0 0
\(151\) −13.7082 −1.11556 −0.557779 0.829990i \(-0.688346\pi\)
−0.557779 + 0.829990i \(0.688346\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −27.4164 −2.20214
\(156\) 0 0
\(157\) −7.52786 −0.600789 −0.300394 0.953815i \(-0.597118\pi\)
−0.300394 + 0.953815i \(0.597118\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.23607 −0.0974158
\(162\) 0 0
\(163\) 12.0000 0.939913 0.469956 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.944272 0.0730700 0.0365350 0.999332i \(-0.488368\pi\)
0.0365350 + 0.999332i \(0.488368\pi\)
\(168\) 0 0
\(169\) 14.4164 1.10895
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −15.8885 −1.20798 −0.603992 0.796991i \(-0.706424\pi\)
−0.603992 + 0.796991i \(0.706424\pi\)
\(174\) 0 0
\(175\) −5.47214 −0.413655
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −4.00000 −0.298974 −0.149487 0.988764i \(-0.547762\pi\)
−0.149487 + 0.988764i \(0.547762\pi\)
\(180\) 0 0
\(181\) 17.2361 1.28115 0.640573 0.767897i \(-0.278697\pi\)
0.640573 + 0.767897i \(0.278697\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −28.9443 −2.12803
\(186\) 0 0
\(187\) −2.11146 −0.154405
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −20.6525 −1.49436 −0.747180 0.664621i \(-0.768593\pi\)
−0.747180 + 0.664621i \(0.768593\pi\)
\(192\) 0 0
\(193\) 1.05573 0.0759930 0.0379965 0.999278i \(-0.487902\pi\)
0.0379965 + 0.999278i \(0.487902\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 9.41641 0.670891 0.335446 0.942060i \(-0.391113\pi\)
0.335446 + 0.942060i \(0.391113\pi\)
\(198\) 0 0
\(199\) −5.52786 −0.391860 −0.195930 0.980618i \(-0.562773\pi\)
−0.195930 + 0.980618i \(0.562773\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0.472136 0.0331374
\(204\) 0 0
\(205\) 6.47214 0.452034
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.763932 −0.0528423
\(210\) 0 0
\(211\) 6.18034 0.425472 0.212736 0.977110i \(-0.431763\pi\)
0.212736 + 0.977110i \(0.431763\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −12.9443 −0.882792
\(216\) 0 0
\(217\) 8.47214 0.575126
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −14.4721 −0.973501
\(222\) 0 0
\(223\) −10.0000 −0.669650 −0.334825 0.942280i \(-0.608677\pi\)
−0.334825 + 0.942280i \(0.608677\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −11.4164 −0.757734 −0.378867 0.925451i \(-0.623686\pi\)
−0.378867 + 0.925451i \(0.623686\pi\)
\(228\) 0 0
\(229\) −18.9443 −1.25187 −0.625936 0.779874i \(-0.715283\pi\)
−0.625936 + 0.779874i \(0.715283\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 20.3607 1.33387 0.666936 0.745115i \(-0.267605\pi\)
0.666936 + 0.745115i \(0.267605\pi\)
\(234\) 0 0
\(235\) 8.00000 0.521862
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −22.7639 −1.47248 −0.736238 0.676723i \(-0.763400\pi\)
−0.736238 + 0.676723i \(0.763400\pi\)
\(240\) 0 0
\(241\) 7.23607 0.466116 0.233058 0.972463i \(-0.425127\pi\)
0.233058 + 0.972463i \(0.425127\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.23607 0.206745
\(246\) 0 0
\(247\) −5.23607 −0.333163
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.472136 −0.0298010 −0.0149005 0.999889i \(-0.504743\pi\)
−0.0149005 + 0.999889i \(0.504743\pi\)
\(252\) 0 0
\(253\) −0.944272 −0.0593659
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −15.5279 −0.968602 −0.484301 0.874902i \(-0.660926\pi\)
−0.484301 + 0.874902i \(0.660926\pi\)
\(258\) 0 0
\(259\) 8.94427 0.555770
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −14.1803 −0.874397 −0.437199 0.899365i \(-0.644029\pi\)
−0.437199 + 0.899365i \(0.644029\pi\)
\(264\) 0 0
\(265\) 27.4164 1.68418
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6.94427 0.423400 0.211700 0.977335i \(-0.432100\pi\)
0.211700 + 0.977335i \(0.432100\pi\)
\(270\) 0 0
\(271\) −7.05573 −0.428605 −0.214302 0.976767i \(-0.568748\pi\)
−0.214302 + 0.976767i \(0.568748\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −4.18034 −0.252084
\(276\) 0 0
\(277\) 23.8885 1.43532 0.717662 0.696392i \(-0.245212\pi\)
0.717662 + 0.696392i \(0.245212\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −26.9443 −1.60736 −0.803680 0.595061i \(-0.797128\pi\)
−0.803680 + 0.595061i \(0.797128\pi\)
\(282\) 0 0
\(283\) −24.9443 −1.48278 −0.741392 0.671073i \(-0.765834\pi\)
−0.741392 + 0.671073i \(0.765834\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.00000 −0.118056
\(288\) 0 0
\(289\) −9.36068 −0.550628
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 10.0000 0.584206 0.292103 0.956387i \(-0.405645\pi\)
0.292103 + 0.956387i \(0.405645\pi\)
\(294\) 0 0
\(295\) −25.8885 −1.50729
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −6.47214 −0.374293
\(300\) 0 0
\(301\) 4.00000 0.230556
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.52786 −0.0874852
\(306\) 0 0
\(307\) −24.3607 −1.39034 −0.695169 0.718847i \(-0.744670\pi\)
−0.695169 + 0.718847i \(0.744670\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4.94427 0.280364 0.140182 0.990126i \(-0.455231\pi\)
0.140182 + 0.990126i \(0.455231\pi\)
\(312\) 0 0
\(313\) 5.05573 0.285767 0.142883 0.989740i \(-0.454363\pi\)
0.142883 + 0.989740i \(0.454363\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −14.0000 −0.786318 −0.393159 0.919470i \(-0.628618\pi\)
−0.393159 + 0.919470i \(0.628618\pi\)
\(318\) 0 0
\(319\) 0.360680 0.0201942
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.76393 0.153789
\(324\) 0 0
\(325\) −28.6525 −1.58935
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2.47214 −0.136293
\(330\) 0 0
\(331\) 14.7639 0.811499 0.405750 0.913984i \(-0.367011\pi\)
0.405750 + 0.913984i \(0.367011\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 16.9443 0.925764
\(336\) 0 0
\(337\) 31.3050 1.70529 0.852645 0.522491i \(-0.174997\pi\)
0.852645 + 0.522491i \(0.174997\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.47214 0.350486
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9.70820 0.521164 0.260582 0.965452i \(-0.416086\pi\)
0.260582 + 0.965452i \(0.416086\pi\)
\(348\) 0 0
\(349\) 28.8328 1.54339 0.771693 0.635996i \(-0.219410\pi\)
0.771693 + 0.635996i \(0.219410\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.70820 0.197368 0.0986839 0.995119i \(-0.468537\pi\)
0.0986839 + 0.995119i \(0.468537\pi\)
\(354\) 0 0
\(355\) −33.8885 −1.79862
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7.70820 0.406823 0.203412 0.979093i \(-0.434797\pi\)
0.203412 + 0.979093i \(0.434797\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −14.4721 −0.757506
\(366\) 0 0
\(367\) −0.944272 −0.0492906 −0.0246453 0.999696i \(-0.507846\pi\)
−0.0246453 + 0.999696i \(0.507846\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −8.47214 −0.439851
\(372\) 0 0
\(373\) 16.3607 0.847124 0.423562 0.905867i \(-0.360780\pi\)
0.423562 + 0.905867i \(0.360780\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.47214 0.127321
\(378\) 0 0
\(379\) 9.81966 0.504402 0.252201 0.967675i \(-0.418846\pi\)
0.252201 + 0.967675i \(0.418846\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −20.9443 −1.07020 −0.535101 0.844788i \(-0.679727\pi\)
−0.535101 + 0.844788i \(0.679727\pi\)
\(384\) 0 0
\(385\) 2.47214 0.125992
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −18.0000 −0.912636 −0.456318 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) 0 0
\(391\) 3.41641 0.172775
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7.41641 0.373160
\(396\) 0 0
\(397\) 10.3607 0.519988 0.259994 0.965610i \(-0.416279\pi\)
0.259994 + 0.965610i \(0.416279\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 22.9443 1.14578 0.572891 0.819631i \(-0.305822\pi\)
0.572891 + 0.819631i \(0.305822\pi\)
\(402\) 0 0
\(403\) 44.3607 2.20976
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6.83282 0.338690
\(408\) 0 0
\(409\) 12.7639 0.631136 0.315568 0.948903i \(-0.397805\pi\)
0.315568 + 0.948903i \(0.397805\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 8.00000 0.393654
\(414\) 0 0
\(415\) 6.47214 0.317705
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 9.41641 0.460022 0.230011 0.973188i \(-0.426124\pi\)
0.230011 + 0.973188i \(0.426124\pi\)
\(420\) 0 0
\(421\) 26.4721 1.29017 0.645086 0.764110i \(-0.276821\pi\)
0.645086 + 0.764110i \(0.276821\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 15.1246 0.733651
\(426\) 0 0
\(427\) 0.472136 0.0228483
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 28.9443 1.39420 0.697098 0.716976i \(-0.254474\pi\)
0.697098 + 0.716976i \(0.254474\pi\)
\(432\) 0 0
\(433\) 16.7639 0.805623 0.402812 0.915283i \(-0.368033\pi\)
0.402812 + 0.915283i \(0.368033\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.23607 0.0591292
\(438\) 0 0
\(439\) 29.4164 1.40397 0.701984 0.712192i \(-0.252298\pi\)
0.701984 + 0.712192i \(0.252298\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.18034 0.198614 0.0993070 0.995057i \(-0.468337\pi\)
0.0993070 + 0.995057i \(0.468337\pi\)
\(444\) 0 0
\(445\) 22.4721 1.06528
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −34.9443 −1.64912 −0.824561 0.565773i \(-0.808578\pi\)
−0.824561 + 0.565773i \(0.808578\pi\)
\(450\) 0 0
\(451\) −1.52786 −0.0719443
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 16.9443 0.794360
\(456\) 0 0
\(457\) −17.4164 −0.814705 −0.407353 0.913271i \(-0.633548\pi\)
−0.407353 + 0.913271i \(0.633548\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 11.2361 0.523316 0.261658 0.965161i \(-0.415731\pi\)
0.261658 + 0.965161i \(0.415731\pi\)
\(462\) 0 0
\(463\) 14.4721 0.672577 0.336289 0.941759i \(-0.390828\pi\)
0.336289 + 0.941759i \(0.390828\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.88854 −0.365038 −0.182519 0.983202i \(-0.558425\pi\)
−0.182519 + 0.983202i \(0.558425\pi\)
\(468\) 0 0
\(469\) −5.23607 −0.241779
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3.05573 0.140503
\(474\) 0 0
\(475\) 5.47214 0.251079
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8.00000 0.365529 0.182765 0.983157i \(-0.441495\pi\)
0.182765 + 0.983157i \(0.441495\pi\)
\(480\) 0 0
\(481\) 46.8328 2.13539
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −10.4721 −0.475515
\(486\) 0 0
\(487\) −10.2918 −0.466366 −0.233183 0.972433i \(-0.574914\pi\)
−0.233183 + 0.972433i \(0.574914\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −41.1246 −1.85593 −0.927964 0.372670i \(-0.878442\pi\)
−0.927964 + 0.372670i \(0.878442\pi\)
\(492\) 0 0
\(493\) −1.30495 −0.0587721
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10.4721 0.469739
\(498\) 0 0
\(499\) −14.4721 −0.647862 −0.323931 0.946081i \(-0.605005\pi\)
−0.323931 + 0.946081i \(0.605005\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 31.7771 1.41687 0.708435 0.705776i \(-0.249401\pi\)
0.708435 + 0.705776i \(0.249401\pi\)
\(504\) 0 0
\(505\) 13.5279 0.601982
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −19.3050 −0.855677 −0.427838 0.903855i \(-0.640725\pi\)
−0.427838 + 0.903855i \(0.640725\pi\)
\(510\) 0 0
\(511\) 4.47214 0.197836
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −53.3050 −2.34890
\(516\) 0 0
\(517\) −1.88854 −0.0830581
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −13.4164 −0.587784 −0.293892 0.955839i \(-0.594951\pi\)
−0.293892 + 0.955839i \(0.594951\pi\)
\(522\) 0 0
\(523\) −33.3050 −1.45632 −0.728162 0.685405i \(-0.759625\pi\)
−0.728162 + 0.685405i \(0.759625\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −23.4164 −1.02003
\(528\) 0 0
\(529\) −21.4721 −0.933571
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −10.4721 −0.453599
\(534\) 0 0
\(535\) −49.8885 −2.15687
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.763932 −0.0329049
\(540\) 0 0
\(541\) −14.9443 −0.642504 −0.321252 0.946994i \(-0.604104\pi\)
−0.321252 + 0.946994i \(0.604104\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −28.9443 −1.23984
\(546\) 0 0
\(547\) −3.70820 −0.158551 −0.0792757 0.996853i \(-0.525261\pi\)
−0.0792757 + 0.996853i \(0.525261\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.472136 −0.0201137
\(552\) 0 0
\(553\) −2.29180 −0.0974571
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −33.4164 −1.41590 −0.707949 0.706263i \(-0.750380\pi\)
−0.707949 + 0.706263i \(0.750380\pi\)
\(558\) 0 0
\(559\) 20.9443 0.885848
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −28.0000 −1.18006 −0.590030 0.807382i \(-0.700884\pi\)
−0.590030 + 0.807382i \(0.700884\pi\)
\(564\) 0 0
\(565\) 35.4164 1.48998
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 36.8328 1.54411 0.772056 0.635555i \(-0.219228\pi\)
0.772056 + 0.635555i \(0.219228\pi\)
\(570\) 0 0
\(571\) 25.5279 1.06831 0.534154 0.845387i \(-0.320630\pi\)
0.534154 + 0.845387i \(0.320630\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6.76393 0.282075
\(576\) 0 0
\(577\) −10.5836 −0.440601 −0.220300 0.975432i \(-0.570704\pi\)
−0.220300 + 0.975432i \(0.570704\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2.00000 −0.0829740
\(582\) 0 0
\(583\) −6.47214 −0.268048
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 14.0000 0.577842 0.288921 0.957353i \(-0.406704\pi\)
0.288921 + 0.957353i \(0.406704\pi\)
\(588\) 0 0
\(589\) −8.47214 −0.349088
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.875388 −0.0359479 −0.0179739 0.999838i \(-0.505722\pi\)
−0.0179739 + 0.999838i \(0.505722\pi\)
\(594\) 0 0
\(595\) −8.94427 −0.366679
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −13.5279 −0.552734 −0.276367 0.961052i \(-0.589130\pi\)
−0.276367 + 0.961052i \(0.589130\pi\)
\(600\) 0 0
\(601\) −45.1246 −1.84067 −0.920336 0.391129i \(-0.872084\pi\)
−0.920336 + 0.391129i \(0.872084\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −33.7082 −1.37043
\(606\) 0 0
\(607\) −10.0000 −0.405887 −0.202944 0.979190i \(-0.565051\pi\)
−0.202944 + 0.979190i \(0.565051\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −12.9443 −0.523669
\(612\) 0 0
\(613\) 11.8885 0.480174 0.240087 0.970751i \(-0.422824\pi\)
0.240087 + 0.970751i \(0.422824\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9.52786 0.383577 0.191789 0.981436i \(-0.438571\pi\)
0.191789 + 0.981436i \(0.438571\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −6.94427 −0.278216
\(624\) 0 0
\(625\) −22.4164 −0.896656
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −24.7214 −0.985705
\(630\) 0 0
\(631\) 32.3607 1.28826 0.644129 0.764917i \(-0.277220\pi\)
0.644129 + 0.764917i \(0.277220\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −36.3607 −1.44293
\(636\) 0 0
\(637\) −5.23607 −0.207461
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 0 0
\(643\) −17.8885 −0.705455 −0.352728 0.935726i \(-0.614746\pi\)
−0.352728 + 0.935726i \(0.614746\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8.94427 0.351636 0.175818 0.984423i \(-0.443743\pi\)
0.175818 + 0.984423i \(0.443743\pi\)
\(648\) 0 0
\(649\) 6.11146 0.239896
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −11.8885 −0.465235 −0.232617 0.972568i \(-0.574729\pi\)
−0.232617 + 0.972568i \(0.574729\pi\)
\(654\) 0 0
\(655\) 27.4164 1.07125
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −23.4164 −0.912174 −0.456087 0.889935i \(-0.650749\pi\)
−0.456087 + 0.889935i \(0.650749\pi\)
\(660\) 0 0
\(661\) −3.70820 −0.144232 −0.0721162 0.997396i \(-0.522975\pi\)
−0.0721162 + 0.997396i \(0.522975\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3.23607 −0.125489
\(666\) 0 0
\(667\) −0.583592 −0.0225968
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0.360680 0.0139239
\(672\) 0 0
\(673\) 29.4164 1.13392 0.566960 0.823746i \(-0.308120\pi\)
0.566960 + 0.823746i \(0.308120\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 33.4164 1.28430 0.642148 0.766580i \(-0.278043\pi\)
0.642148 + 0.766580i \(0.278043\pi\)
\(678\) 0 0
\(679\) 3.23607 0.124189
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 29.8885 1.14365 0.571827 0.820374i \(-0.306235\pi\)
0.571827 + 0.820374i \(0.306235\pi\)
\(684\) 0 0
\(685\) 8.00000 0.305664
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −44.3607 −1.69001
\(690\) 0 0
\(691\) 8.94427 0.340256 0.170128 0.985422i \(-0.445582\pi\)
0.170128 + 0.985422i \(0.445582\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 28.9443 1.09792
\(696\) 0 0
\(697\) 5.52786 0.209383
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 32.8328 1.24008 0.620039 0.784571i \(-0.287117\pi\)
0.620039 + 0.784571i \(0.287117\pi\)
\(702\) 0 0
\(703\) −8.94427 −0.337340
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.18034 −0.157218
\(708\) 0 0
\(709\) −14.0000 −0.525781 −0.262891 0.964826i \(-0.584676\pi\)
−0.262891 + 0.964826i \(0.584676\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −10.4721 −0.392185
\(714\) 0 0
\(715\) 12.9443 0.484088
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) 16.4721 0.613454
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.58359 −0.0959522
\(726\) 0 0
\(727\) 17.8885 0.663449 0.331725 0.943376i \(-0.392369\pi\)
0.331725 + 0.943376i \(0.392369\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −11.0557 −0.408911
\(732\) 0 0
\(733\) 1.05573 0.0389942 0.0194971 0.999810i \(-0.493793\pi\)
0.0194971 + 0.999810i \(0.493793\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4.00000 −0.147342
\(738\) 0 0
\(739\) −7.63932 −0.281017 −0.140508 0.990079i \(-0.544874\pi\)
−0.140508 + 0.990079i \(0.544874\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 17.3050 0.634857 0.317429 0.948282i \(-0.397181\pi\)
0.317429 + 0.948282i \(0.397181\pi\)
\(744\) 0 0
\(745\) −24.3607 −0.892506
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 15.4164 0.563303
\(750\) 0 0
\(751\) −37.1246 −1.35470 −0.677348 0.735663i \(-0.736871\pi\)
−0.677348 + 0.735663i \(0.736871\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −44.3607 −1.61445
\(756\) 0 0
\(757\) −15.8885 −0.577479 −0.288739 0.957408i \(-0.593236\pi\)
−0.288739 + 0.957408i \(0.593236\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −49.5967 −1.79788 −0.898940 0.438071i \(-0.855662\pi\)
−0.898940 + 0.438071i \(0.855662\pi\)
\(762\) 0 0
\(763\) 8.94427 0.323804
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 41.8885 1.51251
\(768\) 0 0
\(769\) −25.0557 −0.903533 −0.451766 0.892136i \(-0.649206\pi\)
−0.451766 + 0.892136i \(0.649206\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −35.3050 −1.26983 −0.634915 0.772582i \(-0.718965\pi\)
−0.634915 + 0.772582i \(0.718965\pi\)
\(774\) 0 0
\(775\) −46.3607 −1.66532
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.00000 0.0716574
\(780\) 0 0
\(781\) 8.00000 0.286263
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −24.3607 −0.869470
\(786\) 0 0
\(787\) 19.4164 0.692120 0.346060 0.938212i \(-0.387519\pi\)
0.346060 + 0.938212i \(0.387519\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −10.9443 −0.389134
\(792\) 0 0
\(793\) 2.47214 0.0877881
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −27.3050 −0.967191 −0.483596 0.875292i \(-0.660669\pi\)
−0.483596 + 0.875292i \(0.660669\pi\)
\(798\) 0 0
\(799\) 6.83282 0.241728
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 3.41641 0.120562
\(804\) 0 0
\(805\) −4.00000 −0.140981
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 12.0000 0.421898 0.210949 0.977497i \(-0.432345\pi\)
0.210949 + 0.977497i \(0.432345\pi\)
\(810\) 0 0
\(811\) 26.2492 0.921735 0.460867 0.887469i \(-0.347538\pi\)
0.460867 + 0.887469i \(0.347538\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 38.8328 1.36025
\(816\) 0 0
\(817\) −4.00000 −0.139942
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 22.3607 0.780393 0.390197 0.920732i \(-0.372407\pi\)
0.390197 + 0.920732i \(0.372407\pi\)
\(822\) 0 0
\(823\) −20.5836 −0.717499 −0.358749 0.933434i \(-0.616797\pi\)
−0.358749 + 0.933434i \(0.616797\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −31.0557 −1.07991 −0.539957 0.841693i \(-0.681559\pi\)
−0.539957 + 0.841693i \(0.681559\pi\)
\(828\) 0 0
\(829\) −32.0689 −1.11380 −0.556899 0.830580i \(-0.688009\pi\)
−0.556899 + 0.830580i \(0.688009\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.76393 0.0957646
\(834\) 0 0
\(835\) 3.05573 0.105748
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 18.8328 0.650181 0.325091 0.945683i \(-0.394605\pi\)
0.325091 + 0.945683i \(0.394605\pi\)
\(840\) 0 0
\(841\) −28.7771 −0.992313
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 46.6525 1.60489
\(846\) 0 0
\(847\) 10.4164 0.357912
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −11.0557 −0.378985
\(852\) 0 0
\(853\) 27.8885 0.954886 0.477443 0.878663i \(-0.341564\pi\)
0.477443 + 0.878663i \(0.341564\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 48.8328 1.66810 0.834049 0.551691i \(-0.186017\pi\)
0.834049 + 0.551691i \(0.186017\pi\)
\(858\) 0 0
\(859\) −19.7771 −0.674786 −0.337393 0.941364i \(-0.609545\pi\)
−0.337393 + 0.941364i \(0.609545\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 12.3607 0.420762 0.210381 0.977619i \(-0.432529\pi\)
0.210381 + 0.977619i \(0.432529\pi\)
\(864\) 0 0
\(865\) −51.4164 −1.74821
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −1.75078 −0.0593910
\(870\) 0 0
\(871\) −27.4164 −0.928970
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.52786 −0.0516512
\(876\) 0 0
\(877\) −23.0557 −0.778537 −0.389268 0.921124i \(-0.627272\pi\)
−0.389268 + 0.921124i \(0.627272\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −57.9574 −1.95264 −0.976318 0.216342i \(-0.930587\pi\)
−0.976318 + 0.216342i \(0.930587\pi\)
\(882\) 0 0
\(883\) −1.52786 −0.0514167 −0.0257084 0.999669i \(-0.508184\pi\)
−0.0257084 + 0.999669i \(0.508184\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −9.88854 −0.332025 −0.166012 0.986124i \(-0.553089\pi\)
−0.166012 + 0.986124i \(0.553089\pi\)
\(888\) 0 0
\(889\) 11.2361 0.376846
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2.47214 0.0827269
\(894\) 0 0
\(895\) −12.9443 −0.432679
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 4.00000 0.133407
\(900\) 0 0
\(901\) 23.4164 0.780114
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 55.7771 1.85409
\(906\) 0 0
\(907\) −24.2918 −0.806596 −0.403298 0.915069i \(-0.632136\pi\)
−0.403298 + 0.915069i \(0.632136\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −7.41641 −0.245717 −0.122858 0.992424i \(-0.539206\pi\)
−0.122858 + 0.992424i \(0.539206\pi\)
\(912\) 0 0
\(913\) −1.52786 −0.0505649
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −8.47214 −0.279775
\(918\) 0 0
\(919\) −14.4721 −0.477392 −0.238696 0.971094i \(-0.576720\pi\)
−0.238696 + 0.971094i \(0.576720\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 54.8328 1.80484
\(924\) 0 0
\(925\) −48.9443 −1.60928
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 40.6525 1.33376 0.666882 0.745163i \(-0.267628\pi\)
0.666882 + 0.745163i \(0.267628\pi\)
\(930\) 0 0
\(931\) 1.00000 0.0327737
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −6.83282 −0.223457
\(936\) 0 0
\(937\) 52.8328 1.72597 0.862986 0.505227i \(-0.168591\pi\)
0.862986 + 0.505227i \(0.168591\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −35.3050 −1.15091 −0.575454 0.817834i \(-0.695175\pi\)
−0.575454 + 0.817834i \(0.695175\pi\)
\(942\) 0 0
\(943\) 2.47214 0.0805038
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 27.8197 0.904017 0.452009 0.892014i \(-0.350708\pi\)
0.452009 + 0.892014i \(0.350708\pi\)
\(948\) 0 0
\(949\) 23.4164 0.760129
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 2.00000 0.0647864 0.0323932 0.999475i \(-0.489687\pi\)
0.0323932 + 0.999475i \(0.489687\pi\)
\(954\) 0 0
\(955\) −66.8328 −2.16266
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −2.47214 −0.0798294
\(960\) 0 0
\(961\) 40.7771 1.31539
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 3.41641 0.109978
\(966\) 0 0
\(967\) −1.16718 −0.0375341 −0.0187671 0.999824i \(-0.505974\pi\)
−0.0187671 + 0.999824i \(0.505974\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 58.2492 1.86931 0.934653 0.355560i \(-0.115710\pi\)
0.934653 + 0.355560i \(0.115710\pi\)
\(972\) 0 0
\(973\) −8.94427 −0.286740
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −44.8328 −1.43433 −0.717164 0.696904i \(-0.754560\pi\)
−0.717164 + 0.696904i \(0.754560\pi\)
\(978\) 0 0
\(979\) −5.30495 −0.169547
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −39.7771 −1.26869 −0.634346 0.773049i \(-0.718731\pi\)
−0.634346 + 0.773049i \(0.718731\pi\)
\(984\) 0 0
\(985\) 30.4721 0.970923
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −4.94427 −0.157219
\(990\) 0 0
\(991\) −44.5410 −1.41489 −0.707446 0.706767i \(-0.750153\pi\)
−0.707446 + 0.706767i \(0.750153\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −17.8885 −0.567105
\(996\) 0 0
\(997\) −4.47214 −0.141634 −0.0708170 0.997489i \(-0.522561\pi\)
−0.0708170 + 0.997489i \(0.522561\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 9576.2.a.bp.1.2 yes 2
3.2 odd 2 9576.2.a.bg.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9576.2.a.bg.1.1 2 3.2 odd 2
9576.2.a.bp.1.2 yes 2 1.1 even 1 trivial